QuestionAccording to a survey in a country, of adults do not own a credit card. Suppose a simple random sample of 400 adults is obtained. Comple
B. Not normal because and
C. Not normal because and
D. Approximately normal because and
Determine the mean of e sampling distribution of .
(Round to two decimal places as needed.)
Determine the standard deviation of the sampling distribution of .
(Round to three decimal places as needed.)
(b) What is the probability that in a random sample of 400 adults, more than do not own a credit card?
The probability is .1056 .
(Round to four decimal places as needed.)
Interpret this probability.
If 100 different random samples of 400 adults were obtained, one would expect 11 to result in more than not owning a credit card.
(Round to the nearest integer as needed.)
(c) What is the probability that in a random sample of 400 adults, between and do not own a credit card?
The probability is
(Round to four decimal places as needed.)
Studdy Solution
STEP 1
1. The proportion of adults who do not own a credit card is .
2. The sample size is .
3. The population size is assumed to be large enough for .
4. The sampling distribution of is approximately normal if .
STEP 2
1. Verify normality conditions for the sampling distribution.
2. Calculate the mean and standard deviation of the sampling distribution of .
3. Calculate the probability for more than not owning a credit card.
4. Calculate the probability for between and not owning a credit card.
STEP 3
Verify the normality conditions:
Since both and are greater than 10, the sampling distribution is approximately normal.
STEP 4
Calculate the mean of the sampling distribution of :
Calculate the standard deviation of the sampling distribution of :
STEP 5
Calculate the probability that more than do not own a credit card:
Convert to a proportion:
Calculate the z-score:
Find the probability using the standard normal distribution table or calculator:
Interpretation: If 100 different random samples of 400 adults were obtained, one would expect approximately 11 samples to result in more than not owning a credit card.
STEP 6
Calculate the probability that between and do not own a credit card:
Convert to a proportion:
Calculate the z-scores:
Find the probability :
Using the standard normal distribution table or calculator:
The probability is:
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